Electronic Journal of Statistics

Change-point detection in the marginal distribution of a linear process

Farid El Ktaibi and B. Gail Ivanoff

Full-text: Open access

Abstract

The subject of this paper is the detection of a change in the marginal distribution of a stationary linear process. By considering the marginal distribution, the change-point model can simultaneously incorporate any change in the coefficients and/or the innovations of the linear process. Furthermore, the change point can be random and data dependent. The key is an analysis of the asymptotic behaviour of the sequential empirical process, both with and without a change point. Our results hold under very mild conditions on the existence of any moment of the innovations and a corresponding condition of summability of the coefficients.

Article information

Source
Electron. J. Statist., Volume 10, Number 2 (2016), 3945-3985.

Dates
Received: October 2015
First available in Project Euclid: 13 December 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1481598074

Digital Object Identifier
doi:10.1214/16-EJS1215

Mathematical Reviews number (MathSciNet)
MR3581958

Zentralblatt MATH identifier
1353.62095

Subjects
Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 62G10, 62G30, 60F17

Keywords
Causal linear process sequential empirical process change-point

Citation

El Ktaibi, Farid; Ivanoff, B. Gail. Change-point detection in the marginal distribution of a linear process. Electron. J. Statist. 10 (2016), no. 2, 3945--3985. doi:10.1214/16-EJS1215. https://projecteuclid.org/euclid.ejs/1481598074


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